The Fifth Circuit has determined that a 237(a)(1)(H) waiver cannot waive inadmissibility stemming from a crime involving moral turpitude committed prior to adjustment of status nor for deportability related a conviction for visa fraud.
The full text of Reese v. Garland can be found here:
https://www.ca5.uscourts.gov/opinions/pub/22/22-60111-CV0.pdf